Direct Imaging of Carrier Funneling in a Dielectric Engineered 2D Semiconductor

In atomically thin transition-metal dichalcogenides (TMDCs), the environmental sensitivity of the strong Coulomb interaction offers promising approaches to create spatially varying potential landscapes in the same continuous material by tuning its dielectric environment. Thus, allowing for control of transport. However, a scalable and CMOS-compatible method for achieving this is required to harness these effects in practical applications. In addition, because of their ultrashort lifetime, observing the spatiotemporal dynamics of carriers in monolayer TMDCs, on the relevant time scale, is challenging. Here, we pattern and deposit a thin film of hafnium oxide (HfO2) via atomic layer deposition (ALD) on top of a monolayer of WSe2. This allows for the engineering of the dielectric environment of the monolayer and design of heterostructures with nanoscale spatial resolution via a highly scalable postsynthesis methodology. We then directly image the transport of photoexcitations in the monolayer with 50 fs time resolution and few-nanometer spatial precision, using a pump probe microscopy technique. We observe the unidirectional funneling of charge carriers, from the unpatterned to the patterned areas, over more than 50 nm in the first 20 ps with velocities of over 2 × 103 m/s at room temperature. These results demonstrate the possibilities offered by dielectric engineering via ALD patterning, allowing for arbitrary spatial patterns that define the potential landscape and allow for control of the transport of excitations in atomically thin materials. This work also shows the power of the transient absorption methodology to image the motion of photoexcited states in complex potential landscapes on ultrafast time scales.

C ontrolling the transport of electronic excitations is central to semiconductor technologies.To this end, several strategies have been developed to tailor the band structure of materials on the nanoscale.This includes spatial variations in the material stoichiometry, 1 strain gradients, 2 or the formation of a heterojunction with different materials. 3ompelling opportunities in band structure design have appeared with the advent of two-dimensional (2D) semiconductors.Because they are atomically thin, they are very sensitive to their environment.For example, strain, 4−14 environmental dielectric screening, 15−25 polarization of ferroelectric substrate, 26,27 and adsorption of chemicals on the surface 28,29 have been shown to have a significant impact on the energetics of the material.This offers the possibility to generate complex potential landscapes, postsynthesis and in the same material, by engineering the material's surroundings. 8,11,14,15,20,26,27,30,31−35 The optical response of a ML TMDC is dominated by excitons because of an unusually strong Coulomb interaction. 36,37The origin of this strong Coulombic interaction is well understood.The electrostatic potential of a charge is screened more or less effectively, depending on the permittivity of the medium in which it is embedded in.For an atomically thin material, this includes the surrounding media, which is usually a low-dielectric material (typically air).The screening of the Coulomb interaction is therefore much lower than in bulk inorganic semiconductors.5][16][17][18][19]21,22,38 Consequently, both the quasiparticle bandgap and the exciton binding energy can be tuned by engineering the local dielectric environment.
Although the consequences of strain gradients on excitonic transport have been extensively studied, 6,8,11,13,14,39−43 the full possibilities offered by dielectric engineering remain underexplored.Specifically, two experimental challenges must be overcome.First, we need scalable ways to pattern the dielectric environment over large areas, rather than simply exfoliating and stacking small areas of arbitrarily shaped graphene or h-BN onto the 2D material to be engineered, as has been done to date.Second, we require tools to understand the dynamics and transport of photoexcitation in these complex potential landscapes.This has been challenging to date, as most studies rely on photoluminescence (PL) microscopy, which lacks both the ultrafast time resolution and the nanoscale spatial precision to study these phenomena on the relevant spatiotemporal scales.Furthermore, PL is insensitive to dark excitons and charges, both of which play major roles in these materials.
Here, we tackle both of these issues and demonstrate the patterning of a WSe 2 monolayer with atomic layer deposition, which in principle allows for arbitrary spatial patterns via a highly scalable methodology.We use this method to pattern areas covered with HfO 2 , a high-dielectric-constant insulating material which significantly alters the dielectric environment around the WSe 2 monolayer.Then, using fs-transient optical absorption microscopy, we directly image the motion of carriers, with high temporal resolution and spatial precision well below the diffraction limit.We observe the unidirectional funneling of charge carriers, from the unpatterned to the patterned areas, over more than 50 nm in the first 20 ps after photoexcitations, with velocities over 2 × 10 3 m/s at room temperature.

RESULTS AND DISCUSSION
Figure 1b shows a micrograph of a representative sample: a monolayer of WSe 2 partially covered by a 15 nm thick HfO 2 film.We chose HfO 2 for its high dielectric constant (ε ≈ 25), 44 and its wide use as a gate oxide in CMOS-compatible technologies.Here, the HfO 2 patch is patterned by e-beam lithography and deposited by ALD as described in detail in Figure 1a. Figure 1c presents an AFM height profile of the junction and its derivative, with a fwhm of ∼50 nm, illustrating the sharpness of the junction (a full AFM map of the junction is presented in Supplementary Note 1).Notably, unlike methods relying on the stamping of materials on the 2D layer, this process is highly scalable and could be easily extended to generate more complex patterns.
In order to understand the effect of the high-dielectric environment on the electronic structure of WSe 2 , we performed scanning confocal photoluminescence (PL) measurements on both the pristine WSe 2 monolayer and the WSe 2 / HfO 2 stack.Representative PL spectra from each side of the junction are presented in Figure 1e.We then extract the energy of the optical gap from the PL spectra obtained over the junction and retrieve the 2D map of the transition energy, as shown in Figure 1d.We observe a clear 17 meV red shift of the excitonic transition on the HfO 2 -covered side compared to the pristine layer.
Since HfO 2 has a large dielectric constant, the screening of the electron−hole interaction in WSe 2 is more effective on the side covered by HfO 2 , which reduces the binding energy and blue-shifts the exciton transition (Figure 1g(ii).At the same time, since the electron−electron interaction is also weaker, the bandgap is reduced.This red-shifts the transition (Figure 1g(iii).Based on previous experimental and theoretical work, we expect the decrease in quasiparticle gap and in the exciton binding energy, on the HfO 2 -covered side, to be of similar magnitude and on the order of 100 meV. 15,21,25,45These two opposite effects almost cancel each other, and in the end, the optical gap is only modified by a small amount (Figure 1g(iv)).We note that the sharp shift in the optical gap is observed only after annealing the sample (see Methods).Prior to annealing, we also observe a red shift of the PL on the HfO 2 -covered flake; however the shifts are larger and not homogeneous and the transition from pristine to covered flake is not sharp (see Supplementary Note 2).This suggests that the ALD process induces strain in the monolayer leading to additional shifts of the optical gap. 46Thermal annealing relaxes strain, and a sharp in-plane junction that strictly follows the HfO 2 patch is created.
To image the transport of excitations in this asymmetric potential landscape, we use a transient reflection microscopy technique.Figure 2a presents a schematic of the experiment.Briefly, a 15 fs pump pulse, focused near the diffraction limit, generates a population of excited states.After a controllable time delay, the transient reflection of the sample is imaged onto a camera with a wide-field probe pulse.More details on the experimental setup are presented in Methods and elsewhere. 47,48In contrast to PL-based imaging, our technique is sensitive to both bright and dark states, and because it relies on optical gating, it exhibits a much faster time resolution.As previously described, differential imaging allows tracking the population of photoexcitations in the material, in time and space, with 50 fs time resolution and few-nanometer precision. 47,48Figure 2b shows the evolution of the transient reflection (ΔR/R) images obtained after exciting the sample at a representative point near the junction where we can clearly see the movement over time of the center of mass of the ΔR/R signal.
In order to quantify this motion, we extract the position of the excited state distribution (X(t), Y(t)) at each time delay by fitting these images with a 2D Gaussian distribution, and we measure the movement of the distribution in the direction perpendicular (ΔX(t) = X(0) − X(t)) and parallel (ΔY(t) = Y(0) − Y(t)) to the junction as illustrated in the inset of Figure 2a.To study how this motion varies depending on where the excitations are launched (i.e., the position at t = 0), we repeat this experiment at various points around the junction.For each starting position (X(0),Y(0)) we extract the ΔX and ΔY shifts after a 5 ps delay to build up the maps presented in Figure 2c.We observe no significant shift (ΔY) of the mean of the distribution in the direction parallel to the junction irrespective of the excitation position, while in the perpendicular direction (ΔX), we measure clear positive and negative shifts for the starting position in the vicinity of the junction.This observation of opposite ΔX shifts on each side of the junction paints a slightly more complex situation than a simple unidirectional funneling of excitations across the junction, and a more detailed analysis is required before conclusions on transport can be drawn.
To understand the origin of these opposite ΔX shifts, we measure the decay dynamics on each side of the junction far from the boundary.As shown in Figure 3a, the two kinetics are well approximated by a bimolecular decay, with a decay rate k HfOd 2 = 1.7 × 10 −2 cm 2 s −1 on the covered side and k pristine = 0.9 × 10 −2 cm 2 s −1 on the pristine side.−51 Since the ΔR/R signal decays faster on the HfO 2 side than on the pristine side, in the absence of any transport, a Gaussian distribution sitting across the junction will appear to move toward the pristine side (ΔX < 0), as illustrated in Figure 3b.This means that the negative shifts do not reflect a movement of the population but rather a change in its spatial profile due to the underlying difference in the decay dynamics on either side of the junction.The measured spatial shifts are therefore due to a combination of two effects: actual transport of excitons in the monolayer and a spatial variation of the decay dynamics.Consequently, the raw ΔX shifts presented here are smaller than the true motion of the excitations in the monolayer.More generally, the raw spatial shifts measured in time-resolved microscopy experiments similar to that presented here (whether based on pump− probe or photoluminescence signals) should not be interpreted as movement of carriers in the material without a spatially resolved analysis of the decay dynamics.
In order to evaluate the actual transport of excitations in the monolayer, we modeled the spatiotemporal evolution of the excited state population across the junction with a drift diffusion model.Considering the excitons as quasiparticles evolving in a potential landscape U(x) and decaying through a  bimolecular recombination with spatially varying decay rate k(x), the exciton population n(r,t) is described by the equation where D is the diffusion coefficient in the monolayer.We m o d e l U a s a s m o o t h s t e p f u n c t i o n , , where erf is the error function, such that ∇U is a Gaussian of variance σ, while k(x) = k pristine + H(x){k pristine − k HfOd 2 }, with H being the Heaviside step function, as illustrated in Figure 4a.Importantly, we fix the annihilation rate k pristine and k HfOd 2 to the values extracted from Figure 3. Next, we model the initial exciton distribution as a Gaussian such that = ( ) , and to simulate the microscope objective point spread function (PSF) the calculated n(r,t) distribution is convolved with another Gaussian, . Finally, we extract the position X(t) of the simulated distribution with the same analysis as that with the measured data described before.Figure 4 compares the measured and simulated data.Figure 4b shows a map of the measured ΔX shift as a function of time and initial position around the junction.Figure 4d presents the time evolution of the amplitude of the measured ΔR/R signal at the same positions.Figure 4c,e shows the corresponding simulation results, in good agreement with the experimental results, for D = 2 cm 2 /s, U 0 = 150 meV, and σ = 55 nm.This simple model therefore confirms the funneling and unidirectional motion of excitations from the pristine side to the HfO 2covered side of the junction.We note that varying D from 0.1 to 10 cm 2 /s but keeping the drift current J = D/k B T ∇(n(t)∇U) constant (i.e., keeping DU 0 constant) does not affect the simulation results significantly (see Supplementary Note 3).This suggests that for the time scale studied here (<20 ps) the effect of the diffusion term is negligible compared to the drift current.
The optical pump used here is centered at 550 nm (2.25 eV) and is well above the free particle gap of monolayer WSe 2 .The pump fluence is 17 μJ/cm 2 , which with an absorption of 10% 52 leads to 4 × 10 12 /cm 2 absorbed photons.Under these conditions, mid-infrared pump probe spectroscopy measurements revealed that excitons form within few hundreds of fs, but about 40% of excitations remain as unbound electrons and holes. 53eported values of diffusion coefficients for excitons in monolayer TMDC range from D = 0.1 cm 2 /s to D = 10 cm 2 / s. 49,54−58 However, even if we assume the largest diffusion constant, a potential step U 0 = 30 meV is required to match the experimental data, and the 17 meV potential step of the excitons, which is lower than the thermal energy (k B T ≈ 25 meV), is too small to drive the observed motion across the junction.Free charges, however, with a potential step across the junction given by the change in quasiparticle gap of about 100 meV are more likely to be driving this motion.Reported mobilities in TMDC are on the order of 100 V cm 2 /s, 33,59 which leads to the diffusion coefficient D ≈ 2.5 cm 2 /s, bringing U 0 to 120 meV, in good agreement with the expected change in the free particle gap across the junction.

CONCLUSION
To summarize, by making use of the sensitivity to the dielectric environment of monolayer TMDC, we have engineered monolayer WSe 2 .We have observed a unidirectional flow of excitations through the junction from the unpatterned to the patterned areas, with shifts of the mean position of excitation higher than 50 nm in 20 ps, leading to a lower bound for the carrier velocity of 2.5 × 10 3 m/s.This simple proof of concept showcases the opportunity offered by 2D semiconductors to engineer potential landscapes to direct excitations and reveals the power of transient absorption microscopy as a technique to observe energy flows in materials on an ultrafast time scale.

METHODS
Sample Preparation.Monolayers of WSe 2 were exfoliated from bulk crystal (HQgraphene) on PDMS films (TELTEC) and transferred on a 170 nm thick glass substrate with a dry transfer technique. 60Electron beam lithography was used to pattern the HfO 2 film.15 nm of gold was evaporated on top of the PMMA resist to act as a discharge layer during the lithography and etch after exposure (gold etchant standard, Sigma-Aldrich).A 15 nm film of HfO 2 was then grown with atomic layer deposition (125 °C, HfCl 4 and H 2 O precursors) before lift-off in acetone.The samples were subsequently annealed in at 200 °C in partial vacuum for 2 h to relax strain.
Transient Absorption Microscopy.Our pump−probe microscopy setup was described previously. 47,48Here, a pump pulse (centered at 550 nm, fluence 17 μJ/cm 2 ) is focused onto the sample with an oil immersion objective (NA = 1.1) to produce a neardiffraction-limited local photoexcitation.After a variable time delay, a copropagating wide-field probe pulse (750 nm, ∼20 μm full width at half-maximum) is reflected on the sample and imaged onto an emCCD camera (Rolera Thunder, QImaging).Wide-field probe images in the presence and absence of the pump excitation are recorded by chopping the pump pulse at 40 Hz.The pump and probe pulses are derived from a Yb:KGW amplifier (1030 nm, 5 W, 200 kHz, 200 fs, LightConversion) via white-light continuous generation and subsequent spectral filtering and compression with chirped mirrors.After transmission through the objective and the glass substrate, the pump is 13 fs, while the probe is 7 fs before the objective.At the sample the probe is significantly chirped, and integrating the signal over a 10 nm spectral bandwidth gives a 50 fs temporal resolution as demonstrated previously. 47icrophotoluminescence.PL spectroscopy was performed on a Renishaw Invia confocal setup equipped with a motorized piezo stage, using an air-cooled Ar-ion 514.5 nm continuous wave (CW) laser via a 100× objective (NA = 0.9).

Figure 1 .
Figure 1.Coulomb engineering in monolayer WSe 2 .(a) Schematic of the heterostructure fabrication process.(b) Micrograph of a representative sample.(c) AFM height profile (black) and its derivative (blue) across the junction.(d) Map of the transition energy extracted from PL spectra.(e) Representative photoluminescence spectra on each side of the junction.(f) Schematic of the sample architecture.(g) Schematic of the energy levels and the effect of the different interaction terms on the different electronic transitions (see main text for details).

Figure 2 .
Figure 2. Imaging of the ultrafast transport.(a) Schematic of the pump−probe microscopy experiment.See main text for details.(b) Time evolution of the transient reflection signal after excitation at a representative point near the boundary.(c) Map of the extracted shifts of the excited state population in the direction perpendicular to the junction (ΔX) and parallel to the junction (ΔY) after a 5 ps delay, as a function of the excitation position.The boundary is located at x = 0 as illustrated in the top panel.

Figure 3 .
Figure 3.Effect of the spatially varying kinetics.(a) Decay kinetics of the ΔR/R signal far from the boundary on the pristine side (blue dots) and the HfO 2 -covered side (orange triangles).Solid lines are fits to a bimolecular decay, describing exciton−exciton annihilation.(b) Simulated Gaussian profile decaying through a bimolecular decay with a spatially dependent decay rate.The decay rate follows the step function illustrated in the top panel with values of K WSed 2 and K HfOd 2 extracted from (a).The profiles are convoluted with a Gaussian to simulate the point spread function of the microscope.

Figure 4 .
Figure 4. Unidirectional exciton funnelling.(a) Schematic of the modeled potential step U and annihilation rate K across the junction.(b) Map of the ΔX shift as a function of time and excitation position near the junction.(c) Corresponding simulated map.(d) Temporal variation of ΔR/R corresponding to the map in (b).(e) Corresponding simulated ΔR/R.